The fundamental question of Distance Geometry, the Distance Geometry Problem (DGP), consists on determining point positions in $\mathbb{R}^K$ such that their Euclidean distances match those in a given list of interpoint distances. If $K=3$, it is called Molecular DGP (MDGP). Under assumptions on the available distances in this list, the search space for the MDGP can be discretized so that it is able to be designed as a binary tree, giving birth to the Discretized MDGP (DMDGP). The main method to solve it is the Branch-and-Prune(BP) Algorithm, a recursive and combinatorial tool that explores such tree in a depth-first search and whose classical formulation is based in a homogeneous matrix product that encodes one translation and two rotations. In the present talk, we present a new formulation for BP using quaternion rotations instead of matrices. We also display some simulations with protein structures from the worldwide Protein Data Bank (wwPDB) for both of the approaches.